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A345953
Number of ways to tile a 2 X n strip with squares and P-shaped pentominos.
1
1, 1, 1, 5, 9, 15, 37, 75, 145, 311, 641, 1295, 2689, 5543, 11345, 23383, 48145, 98903, 203521, 418791, 861169, 1771543, 3644513, 7496231, 15419985, 31720375, 65248385, 134217351, 276091313, 567924823, 1168234977, 2403096999, 4943230993, 10168353527, 20916591169
OFFSET
0,4
COMMENTS
a(n) is also the number of ways to tile a 1 X n strip with squares, four colors of trominos, and 2 colors of pentominos.
FORMULA
a(n) = a(n-1) + 4*a(n-3) + 2*a(n-5).
Sum_{k=0..n} a(k) = (a(n+5) - 4*a(n+2) - 4*a(n+1) - 1)/6.
G.f.: -1/(2*x^5+4*x^3+x-1).
EXAMPLE
Here is a demonstration that a(3) = 5.
._____. ._____. ._____. ._____. ._____.
|_|_|_| | |_| |_| | |_ | | _|
|_|_|_| |_____| |_____| |_|___| |___|_|
MATHEMATICA
LinearRecurrence[{1, 0, 4, 0, 2}, {1, 1, 1, 5, 9}, 40];
CROSSREFS
Sequence in context: A373848 A062516 A249331 * A075133 A351826 A066081
KEYWORD
nonn,easy
AUTHOR
Drisana Bhatia and Greg Dresden, Jun 29 2021
STATUS
approved